Check ur memory;take out and clean if necessary.remove hard drive and replace making sure its seated properly.
check inverter board,vga connections.
try booting from cd(make sure os in drive before boot)to see if any response on screen.
try using ext monitor.
if all these fail have either motherboard fault or screen fault,if screen wont switch motherboard fault

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Take out the battery, plug it in turn it on, if the problem is the same unplug it. Turn it over and remove the access panel from the bottom. There you should find your RAM if you have two RAM modules installed remove both and replace them one at a time with the power off. So insert one and power on computer if the same result as before, remove it and insert the other RAM and power it on again. Also look to see if your CPU fan is spinning. If your fan only spins for 5 to 10 seconds and powers off one of three things are bad, either your CPU, GPU, or Motherboard are bad or damaged. It might turn on here or there if this happens it's probably your GPU. Hope this helps you.

have a look on the bottom of the case for access panels, remove these and check the fans for dust build up, even if the dust doesn't look too bad, its worth cleaning. Also try to remove the fan to check between that and the heatsink, dust can build up there very much. This could cause the fan to be innefficient so could be an overheating problem causing your shutdown.

Try reseating the memory and if that doesn’t work, install the 512’s one at a time to see if one might be defective. If the laptop still won’t turn on, reinstall original memory and see if laptop powers on.Your responses are intended to improve the level of service provided. Please show your appreciation by rating your experience.Thank You.